Geodesic
Diffraction by a narrow circular cone as by a strongly elongated body
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 41, Tome 393 (2011), pp. 12-22

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Leading order terms of the asymptotic expansions in the problems of acoustic and electromagnetic waves diffraction by narrow circular cone are constructed in this paper. By analogy with problems of diffraction by strongly elongated bodies the derivations are carried out in special system of coordinates related to the surface which takes into account that the cone angle is small. Graphics of special functions appearing in the considered problems of diffraction are presented. 
@article{ZNSL_2011_393_a1,
     author = {I. V. Andronov and D. Bouche},
     title = {Diffraction by a narrow circular cone as by a strongly elongated body},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {12--22},
     publisher = {mathdoc},
     volume = {393},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2011_393_a1/}
}
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I. V. Andronov; D. Bouche. Diffraction by a narrow circular cone as by a strongly elongated body. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 41, Tome 393 (2011), pp. 12-22. http://geodesic.mathdoc.fr/item/ZNSL_2011_393_a1/